There has been known a so-called strip build construction method for manufacturing a green tire by repeatedly winding a strip rubber having a predetermined cross sectional shape around a surface of a molding drum (for example, Japanese Unexamined Patent Publication No. 2004-358738). In accordance with this strip build, for example, it is possible to form a tire member having a desired cross sectional shape by sequentially laminating the strip rubber having a thin rectangular cross sectional shape on the molding drum. In the conventional art mentioned above, there is employed a rubber mixing extruder using a gear pump, and it is possible to continuously extrusion mold the strip rubber having the predetermined cross sectional shape. Further, a strip build construction method using an injection molding machine is disclosed, for example, in Japanese Unexamined Patent Publication No. 2001-72335.